Sr Examen
Integral de sin(x^2+4) dx
Solución
Ha introducido
[src]
1 / | | / 2 \ | sin\x + 4/ dx | / 0
$$\int\limits_{0}^{1} \sin{\left(x^{2} + 4 \right)}\, dx$$
Integral(sin(x^2 + 4), (x, 0, 1))
Solución detallada
-
Añadimos la constante de integración:
FresnelSRule(a=1, b=0, c=4, context=sin(x**2 + 4), symbol=x)
Respuesta:
Respuesta (Indefinida)
[src]
/ / ___\ / ___\ \
___ ____ | |x*\/ 2 | |x*\/ 2 | |
/ \/ 2 *\/ pi *|cos(4)*S|-------| + C|-------|*sin(4)|
| | | ____| | ____| |
| / 2 \ \ \ \/ pi / \ \/ pi / /
| sin\x + 4/ dx = C + ----------------------------------------------------
| 2
/
$$\int \sin{\left(x^{2} + 4 \right)}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} \left(\sin{\left(4 \right)} C\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right) + \cos{\left(4 \right)} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)\right)}{2}$$
Gráfica
Respuesta
[src]
/ / ___ \ / ___ \ \
___ ____ | |\/ 2 | |\/ 2 | |
\/ 2 *\/ pi *|cos(4)*S|------| + C|------|*sin(4)|
| | ____| | ____| |
\ \\/ pi / \\/ pi / /
--------------------------------------------------
2
$$\frac{\sqrt{2} \sqrt{\pi} \left(\sin{\left(4 \right)} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) + \cos{\left(4 \right)} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right)\right)}{2}$$
=
=
/ / ___ \ / ___ \ \
___ ____ | |\/ 2 | |\/ 2 | |
\/ 2 *\/ pi *|cos(4)*S|------| + C|------|*sin(4)|
| | ____| | ____| |
\ \\/ pi / \\/ pi / /
--------------------------------------------------
2
$$\frac{\sqrt{2} \sqrt{\pi} \left(\sin{\left(4 \right)} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) + \cos{\left(4 \right)} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right)\right)}{2}$$
sqrt(2)*sqrt(pi)*(cos(4)*fresnels(sqrt(2)/sqrt(pi)) + fresnelc(sqrt(2)/sqrt(pi))*sin(4))/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.